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Over the last two years I have applied for three American Express cards,
2x Amex gold and 1xBA no fee regular card.
All these cards have ended with the same last 4 numbers. Obviously I will not disclose these.
Does this sequence denote any reason or is it purely random? I know it sounds lame but I would like to keep up this streak

I have the Platinum charge card, Nectar credit card and have in the past held the PRG charge. Never had the same numbers. Given that the statement notification emails only identify the card by the last numbers, it seems that you've been struck by an unfortunate coincidence. Maybe life is telling you to buy a lottery ticket!

AA is 37 denoting Amex
BB is 42 for the UK Amex Gold
BB is 17 for the UK BA Amex

CCCCCCC is the Amex account number

D is 1 for the first card type issued under that account.

If you upgraded the Amex Gold to Platinum, or downgraded it to green, or upgraded the BA card to the BAPP card, without cancelling it, CCCCCCC would remain the same and D would become 2. (Though Amex treats it as a new application and potentially you could be declined and be forced to cancel the card.)

EE will be 00 for the main cardholder. If you get supplementary cards, they will be numbered 01 and so on. When your cards expire and you get new ones, the number may go up too, not sure as I've never kept the same Amex for that long.

F is a validation digit which is calculated by applying a formula to the first 14 digits.

Thus if it's the first card and first account, digits 12-14 will be 100.

I think digit 15 has an equal chance of being anything, but this would depend on whether the account numbers have a random distribution or follow a pattern.

Thus there is a 1 in 10 chance that the second card would have the same check digit as the first card, and a 1 in 10 chance that the third card would have the same digit as the first two, so overall a 1/100 chance of this happening to a person who makes a fresh application for 3 different Amexes and is the main cardholder.

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